1. Statement of the Technical Field
The inventive arrangements relate generally to methods and apparatus for providing increased design flexibility for RF circuits, and more particularly to a variably tunable waveguide.
2. Description of the Related Art
A waveguide is a transmission line structure that is commonly used for microwave signals. A waveguide typically consists of a hollow tube made of an electrically conductive material, for example copper, brass, steel, etc., and can be provided in a variety of shapes. Most often waveguides have a rectangular or circular cross section.
In operation, waveguides propagate modes above a certain cutoff frequency (fc). In a waveguide which has a rectangular cross section, the signal wavelength (λc) at the cutoff frequency is given by the equation             λ      c        =          1                                                  (                              m                                  2                  ⁢                                                                           ⁢                  a                                            )                        2                    +                                    (                              n                                  2                  ⁢                                                                           ⁢                  b                                            )                        2                                ,where m,n are mode numbers, a is a width of the wider side of the waveguide, and b is a width of the waveguide measured along the narrow side. The lowest frequency mode in a waveguide is the TE10 mode. In this mode, the equation for the signal wavelength at the cutoff frequency reduces to λc=2a. Further, the relationship between fc and λc, is given by the equation             f      c        =          ν              λ        c              ,where ν is the propagation velocity of a signal within the waveguide. Accordingly, the equation for the cutoff frequency becomes             f      c        =                  ν                  2          ⁢                                           ⁢          a                    =              c                  2          ⁢                                           ⁢          a          ⁢                                                    μ                r                            ⁢                              ɛ                r                                                          ,where μr is the relative permeability within the waveguide and εr is the relative permittivity within the waveguide. Below the cutoff frequency, the attenuation is given by       α    =          54.6      ⁢              l                  λ          c                    ⁢                        1          -                                    (                              f                                  f                  c                                            )                        2                                ,where α is attenuation measured in decibels (dB), l is the length of the waveguide, and f is the frequency at which the attenuation is being calculated.
A waveguide typically has fixed dimensions, and the permittivity and permeability are usually constant. Hence, the cutoff frequency and attenuation characteristics of a waveguide usually are fixed, thus limiting the flexibility of waveguides for use in RF applications.